Functions with a closed graph
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- by Ivan Baggs PDF
- Proc. Amer. Math. Soc. 43 (1974), 439-442 Request permission
Abstract:
Let $X$ be a ${T_2}$ Baire space. A set $F \subset X$ is closed and nowhere dense in $X$ if $F$ is the set of points of discontinuity of a function with a closed graph from $X$ into ${R^n}$. Although the converse does not hold in general, it does hold when $X$ is the real line.References
- Richard Bolstein, Sets of points of discontinuity, Proc. Amer. Math. Soc. 38 (1973), 193–197. MR 312457, DOI 10.1090/S0002-9939-1973-0312457-9
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- Edwin Hewitt and Karl Stromberg, Real and abstract analysis. A modern treatment of the theory of functions of a real variable, Springer-Verlag, New York, 1965. MR 0188387
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 439-442
- MSC: Primary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0334132-8
- MathSciNet review: 0334132